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Geometric Properties Of The Markov And Lagrange Spectra
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Book Synopsis Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by : Sébastien Ferenczi
Download or read book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics written by Sébastien Ferenczi and published by Springer. This book was released on 2018-06-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Book Synopsis Theorems of the 21st Century by : Bogdan Grechuk
Download or read book Theorems of the 21st Century written by Bogdan Grechuk and published by Springer. This book was released on 2019-06-15 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.
Book Synopsis Waves in Complex Media by : Luca Dal Negro
Download or read book Waves in Complex Media written by Luca Dal Negro and published by . This book was released on 2022-05-04 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics.
Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti
Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by Springer Science & Business Media. This book was released on 2004-09-30 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically. Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for "most" dynamical systems, recovering as much as possible of the conclusions of the uniformly hyperbolic case, in great generality. This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed at researchers, both young and senior, willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.
Book Synopsis The Markoff and Lagrange Spectra by : Thomas W. Cusick
Download or read book The Markoff and Lagrange Spectra written by Thomas W. Cusick and published by American Mathematical Soc.. This book was released on 1989 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
Download or read book Acta Arithmetica written by and published by . This book was released on 2011 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov
Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Book Synopsis Probability on Graphs by : Geoffrey Grimmett
Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Book Synopsis Spectra of Graphs by : Dragoš M. Cvetković
Download or read book Spectra of Graphs written by Dragoš M. Cvetković and published by . This book was released on 1980 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.
Book Synopsis Cluster Algebras and Poisson Geometry by : Michael Gekhtman
Download or read book Cluster Algebras and Poisson Geometry written by Michael Gekhtman and published by American Mathematical Soc.. This book was released on 2010 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book devoted to cluster algebras, this work contains chapters on Poisson geometry and Schubert varieties; an introduction to cluster algebras and their main properties; and geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.
Book Synopsis Spectra of Graphs by : Andries E. Brouwer
Download or read book Spectra of Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2011-12-17 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Book Synopsis Reviews in Number Theory, 1984-96 by :
Download or read book Reviews in Number Theory, 1984-96 written by and published by . This book was released on 1997 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Large Eigenvalue Problems by : Yousef Saad
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Book Synopsis Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects by : Davi Dos Santos Lima
Download or read book Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects written by Davi Dos Santos Lima and published by World Scientific. This book was released on 2020-09-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry. Besides presenting many classical results, the book includes several topics of recent research on the subject, connecting several fields of Mathematics — Number Theory, Dynamical Systems and Fractal Geometry.It includes topics as:
Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov
Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un
